Finite Group Databasebeta

#347×Dic83 #35319230

order21248
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C42

Aliases

direct product#347×Dic83

Splittings

SylowC83 ⋊ C4×#347

Subgroups

subgroupG/H
centerC2×C4C42×D83
commutatorC4×C83C43
FrattiniC22×C8C22×D83
FittingC2×#347×C83C2
socleC22×C83C2×#97
prime radicalC23×C83C2×M16
cosocleC22×C8×C83C23
hypercenterC2×#347D83
hypocenterC83C4×#347
LCSG ▷ C4×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×#347

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 84394);